On only 10 acres, you won't be able to have too many cattle. Truthfully, for long term grazing, I would want about 1 head per 3 acres (but I'm used to my area that doesn't have much grass and what we do have spends all summer burned to a crisp). If the irrigated portion is really good grass, I might go 1 head per 2 acres...so 5 head total. I am absolutely phobic about over-grazing grassland when you're trying to feed cattle so I tend to go on the conservative side.
I agree with the poster that said if you're wanting to raise for meat, do not get a dairy breed. Their meat is poorer quality and they don't get as big as beef cattle. Angus or Hereford would be my choice. Some folks around here have "Brangus" cattle, which are Brahman/Angus crosses. They make good meat but they tend to be sort of wild.
Personally, I would start by getting a couple of weanlings (6-10 months old). They are old enough that they don't really require any special care or housing, they can withstand the elements better than a younger one and you aren't as likely to get attached to one that you don't have to hand feed. Just turn them out and let them graze/grow until it's time to butcher.